Probabilistic World

The Birthday Problem: Python Simulation

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UEFA Nations League semi-final between Netherlands and England (prematch, 06/06/2019), with Python code related to the birthday problem in the background

In my last post, I introduced you to the so-called birthday problem. Namely, the probability of having at least one birthday coincidence in a random group of people. I showed you how to approach the question analytically by deriving a simple formula for calculating this probability.

In this post, I want to show you an alternative way of getting the same probability using a computer simulation with the programming language Python!

This post is part of my series Probability Questions from the Real World.

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The Birthday Problem: Analytic Solution

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UEFA Nations League semi-final between Netherlands and England (prematch, 06/06/2019), with the birthday problem formula in the background

Welcome to the first post from my new series. Here we’re going look at a famous probability question often called the birthday problem. This is actually a more general question related to the probability of at least one coincidence after a fixed number of draws from a discrete uniform distribution.

This post is part of my series Probability Questions from the Real World.

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Occam’s Razor: A Probabilistic View

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The word simple written by blocks of "complex" words

“Simple explanations are better than complex explanations.” — have you heard this statement before? It’s the most simplified version of the principle called Occam’s razor. More specifically, the principle says:

A simple theory is always preferable to a complex theory, if the complex theory doesn’t offer a better explanation.

Does it make sense? If it’s not immediately convincing, that’s okay. There have been debates around Occam’s razor’s validity and applicability for a very long time.

In this post, I’m going to give an intuitive introduction to the principle and its justification. I’m going to show that, despite historical debates, there is a sense in which Occam’s razor is always valid. In fact, I’m going to try to convince you this principle is so true that it doesn’t even need to be stated on its own.

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Predicting the 2016 US Presidential Election

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Trump, Johnson, Clinton, and Stein with an American flag in the background.

November 7 UPDATE: click here to view our final update post where we give our latest analyses just a day before the election!
Click here to go to our daily predictions page.

In the first 10 posts I mostly concentrated on theoretical topics. But the general focus of this blog is much broader. For the first time I’m going to show an actual application of probability theory for estimating real life events.

An ongoing event many people are closely following right now is the US presidential election. The primary season officially concluded at the end of July and now the general election battle is in full swing. The main clash is between former Secretary of State Hillary Clinton (D) and businessman Donald Trump (R). Clinton and Trump are challenged by 3rd party candidates Gary Johnson from the Libertarian Party (a two-time former governor of New Mexico) and Jill Stein from the Green Party (a physician and a political activist).

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Coin Bias Calculation Using Bayes’ Theorem

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An ancient Greek coin with an unusual shape and lopsidedness

Why do people flip coins to resolve disputes? It usually happens when neither of two sides wants to compromise with the other about a particular decision. They choose the coin to be the unbiased agent that decides whose way things are going to go. The coin is an unbiased agent because the two possible outcomes of the flip (heads and tails) are equally likely to occur.

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